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31 Mar 2023, 08:45
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:14) correct
24%
(01:20)
wrong
based on 101
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(|x|+x <2\) ?
(1) \(x>-1\)
(2) \(x<0\)
(1) \(x>-1\)
(2) \(x<0\)
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
31 Mar 2023, 09:03
Kudos
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Bunuel
Statement 1
(1) \(x>-1\)
x = 0 ; |x| + x < 2 -- Yes !
x = 1 ; |x| + x < 2 -- No!
As we have two contradicting answers to the question, the statement alone is not sufficient.
We can eliminate A and D.
Statement 2
(2) \(x<0\)
When x < 0, |x| = -x
-x + x = 0
Is \(|x|+x <2\) -- Yes !
The statement is sufficient to answer the question.
Option B
31 Mar 2023, 10:46
Kudos
Bookmarks
Bunuel
Question stem, rephrased:
Is |x| < 2-x ?
Statement 1: x>-1
If x=0, then |x|=0 and 2-x=2, so the answer to the rephrased question stem is YES.
If x=1, then |x|=1 and 2-x=1, so the answer to the rephrased question stem is NO.
INSUFFICIENT.
Note:
|x| = the distance between x and 0
|x-y| = the distance between x and y
Statement 2: x<0
Here, 2-x is POSITIVE, with the result that 2-x = |2-x|=|x-2|.
Question stem, rephrased:
Is |x| < |x-2|?
In words:
Is x closer to 0 than to 2?
Since x is negative, the answer is YES.
SUFFICIENT.
